Storage and attenuation structure 10 for a drainage system, having upper layer 11 with fluid storage recesses 13 and openings 15 located above the storage recesses 13 to allow overflow fluid to drain, and lower layer 12 receiving fluid drained from upper layer 11 and having drainage pathways 14 to collect and drain the fluid received. Drainage pathways 14 are in fluid communication with space 17 between fluid storage recesses 13 such that said space 17 provides additional fluid storage capacity. A filter layer 19 may be provided. Structure 10 may be part of a drainage system supporting a growing medium, and sitting on a roof, for example a green roof. The layers 11, 12 may provide a drainage peak flow attenuation effect, and drainage pathways 14 may direct to an outflow controller. An outflow controller 100 is also described, having a flow controlling restrictor 110 and a drain component 120.